Question

Угол B в равнобедренной трапеции ABCD в 4 раза больше угла D . Найти угол A. Ответ в градусах

Answer 1

Угол D =A, поэтому 180 градусов = 1x+3x= 4x= 180:4=45. 45градусов= угол B+ C, а угол A+D= 45*3= 135 градусов, а тк трапеция равнобедренная, то угол А= 135:2= 67,5 градусов

Answer 2

Finding the Angle A in an Isosceles Trapezoid

To find the angle A in an isosceles trapezoid ABCD, where angle B is four times larger than angle D, we can use the fact that the sum of the interior angles of a trapezoid is equal to 360 degrees.

Let's denote angle A as x, angle B as 4x, angle C as 4x, and angle D as x.

The sum of the interior angles of a trapezoid is given by the equation:

x + 4x + 4x + x = 360

Simplifying the equation, we have:

10x = 360

Dividing both sides of the equation by 10, we find:

x = 36

Therefore, angle A is equal to 36 degrees.

Answer: The angle A in the isosceles trapezoid ABCD is 36 degrees.